The correct answer is $\boxed{\frac{1}{12}^{{\text{th}}}}$ of the span.
A jack arch floor is a type of floor that is constructed using jack arches. Jack arches are small, semi-circular arches that are used to support the weight of the floor above. The rise of a jack arch is the distance from the base of the arch to the apex of the arch. The span of a jack arch is the distance between the two supports of the arch.
The rise of a jack arch is typically kept to $\frac{1}{12}^{{\text{th}}}$ of the span. This is because this ratio provides the best balance between strength and economy. A smaller rise would make the arch weaker, while a larger rise would make the arch more expensive to construct.
The other options are incorrect because they do not represent the typical rise of a jack arch. Option A, $\frac{1}{6}^{{\text{th}}}$ of the span, is too small and would make the arch weaker. Option B, $\frac{1}{8}^{{\text{th}}}$ of the span, is too small and would also make the arch weaker. Option C, $\frac{1}{{10}}^{{\text{th}}}$ of the span, is too large and would make the arch more expensive to construct. Option D, $\frac{1}{{12}}^{{\text{th}}}$ of the span, is the correct ratio that provides the best balance between strength and economy.